Download Mitigation of Magnetizing Inrush Current using Sequential Phase

ISSN 1392 – 1215
ELECTRONICS AND ELECTRICAL ENGINEERING
ELEKTRONIKA IR ELEKTROTECHNIKA
2011. No. 2(108)
ELECTRICAL ENGINEERING
T 190 ņņņņņņņņņņņņņņņņņņņņņ
ELEKTROS INŽINERIJA
Mitigation of Magnetizing Inrush Current using Sequential Phase
Energization Technique
M. Jamali, M. Mirzaie, S. Asghar-Gholamian
Department of Electrical and Computer Engineering, Babol University of Technology,
P. O. Box. 484, Shariaty Ave., Babol, Iran, phone: +981113239214, email: [email protected]
In this paper, the sequential phase energization
technique has been used to mitigate magnetizing inrush
current. Because, the size of the resistor which is
connected to the neutral point of the transformer, has an
important role, analytical formulas have been derived to
calculate inrush current amplitude with a neutral resistor.
To verify the validity of the analytical formulas, a
MATLAB program has been written and the sizes of the
neutral resistor for different inrush current reduction ratios
in a typical transformer have been obtained and then
implemented in MATLAB SIMULINK.
Introduction
Inrush current is a well-known transient current that
may occur when an unloaded or lightly loaded transformer
is energized. The amplitude and shape of the inrush current
depend on several factors such as switching time, remanent
flux, impedance of the system from which the transformer
is energized and etc. [1]. Because the magnitude of this
current can be as high as short circuit currents, many
researches have been conducted to assess and limit the
amplitude and impact of these currents. In [2], transformer
nonlinearities during transient and unbalanced conditions
like inrush current is simulated using separate magnetic
and electric equivalent circuits and then nonlinear
mathematical model is carried out using Newton-Raphson
iterative method. For the simulation of the magnetizing
currents, [3] is developed a model from the structural
parameters of the transformer. In [4], a new model using
wavelet filter bank is presented and transient phenomena
like inrush current are simulated. For modeling transformer
core including hysteresis, [5] used Jiles-Atherton theory
with variable parameters. In [6], a computational technique
is used to calculate inrush current at various switching
conditions and the effects of some parameters like
switching angle, energizing circuit impedance and
remanent flux on the inrush current characteristics are
discussed. Also, limiting and canceling inrush currents
have been investigated in the literature. In [7], a virtual air
gap which equivalent thickness varies in function of
controllable parameters is used to reduce inrush current in
a single phase transformer. In [8] an altered winding coil
distribution is proposed to restrain inrush current with
appropriate voltage regulation and short circuit current.
Sequential phase energization technique is documented in
[9–11]. In this technique, each phase of a three-phase
transformer is energized in sequence with some delays
between them, while a suitable neutral resistor is placed at
the neutral point. In [12–13], a controlled switching with
considering core flux transients has been used to eliminate
inrush current.
Sequential Phase Energization Technique
It is well-known that the inrush currents are highly
unbalanced among three phases. If a transformer is Y
grounded at the energization side, its neutral will also
contain the inrush current. So, it can be expected that the
insertion a resistor into the transformer neutral, may reduce
the magnitude of the magnetizing inrush current. The basic
idea of the sequential phase energization is shown in Fig. 1
where, Va, Vb and Vc are phase voltages and RN is
grounding resistor. Also, ta, tb and tc are the closing times
of the breakers where, tc>tb>ta.
ta
Va
Vc
tb
Vb
tc
RN
Fig. 1. Sequential phase energization scheme with a grounding
resistor
As stated in [9], a simultaneous closing of all threephase breakers does not produce considerable reduction on
67
the inrush currents. So, for improving the results, closing
each phase of the breaker in sequence with some delays
between them was proposed. With this way, the neutral
resistance can behave as a series resistor and this method
can effectively reduce the magnitude of inrush current.
Also, it should be noted that because the neutral current in
normal system operation is close to zero, the bypass
breaker may not be needed or can have a low rating.
(4)
Also, with considering V(t)=VmVLQȦWș, the
following recursive equations for the calculation of the
current and flux in a transformer can be achieved:
Calculation of inrush current with a neutral resistor
It has been found that the peak of inrush current in
the first phase energization is the highest among the three
phases [11]. So, the size of the neutral resistor for a
specific inrush current reduction ratio can be calculated
upon the first phase energization. In the first phase
energization, the equivalent circuit of the unloaded
transformer with a neutral resistor can be shown as Fig. 2
where, RS, LS, RP, RN and V(t) are series resistance, series
inductance, core loss resistance, neutral resistance and
input source, respectively. Also, the magnetizing branch in
the equivalent circuit of the transformer has been presented
with imȜ where, Ȝis the linkage flux.
RS
(5)
LS
RP
(6)
im(Ȝ)
V(t)
where ǻW= tj – tj-1 and ij DUFWJȦĮ.
(5) and (6) have been used to calculate the size of the
neutral resistor to achieve a specific inrush current
reduction ratio. The procedure for calculation a specific
inrush current reduction ratio is described in Fig. 3. It
should be noted that inrush current reduction ratio has been
calculated with (7)
RN
Fig. 2. Equivalent circuit of the transformer with neutral resistor
For the circuit shown in Fig. 2, the following
equations can be written in the primary side of the
transformer:
,
.
(7)
(1)
(2)
Simulation results
Because in the actual transformer, imȜ is nonlinear,
the equations (1) and (2) result into a system of nonlinear
ordinary differential equations. For solving these
equations, we can discrete time t into j intervals. These
equations can be successively integrated from t=0 until
W MǻW with considering imȜ is constant in every ǻW interval.
So, integrating equations (1) and (2) in the intervals tj-1 and
t (tj-1<t<tj) results into equations (3) and (4), where, ĮŁ
(RP+RS+RN)/LS and ȕŁRP/LS:
In this section, for investigation of inrush current
reduction ratio, a three-phase transformer consisted of
single-phase
transformers
is
considered.
These
transformers are connected in Yg-ǻ 7KH SDUDPHWHUV RI
single-phase (220/120) V, 50Hz, 120VA transformers are
RS=15.476ŸLS=12mH, RP=7260Ÿ$OVRWKHPDJQHWL]LQJ
current versus linkage flux is as follow
(8)
Fig. 4 shows the inrush current waveforms for
different phases when no mitigation method is used. As
seen from the figure, the highest amplitude of inrush
current among three phases has been appeared in the phase
A that is 1.437A.
(3)
For calculation the neutral resistor size for a specific
inrush current reduction ratio a program based on the
analytical formulas has been written in MATLAB M-File.
Fig. 5 shows the inrush current waveforms when sequential
68
phase energization technique with RN=345.6Ÿ KDV EHHQ
used. The size of the neutral resistor has been obtained for
a 30% inrush current reduction ratio. As seen from the
figure, with selection a suitable RN, the peak of the inrush
current in phase A has been decreased to 30% (0.431A).
Also, it should be noted that a 1 second delay between
each switching stage has been used to allow phase fluxes
to lose most of the dc component.
(lower amount of inrush current reduction ratio) a larger
neutral resistor is needed.
Calculation the peak of inrush current
using (5) and (6) with RN=0
RN=Rint.
Calculation the peak of inrush current
using (5) and (6) with the new RN
Change the value of
RN
No
Fig. 5. Mitigation of inrush current with sequential phase
energization technique
Calculation of inrush current
reduction ratio
The desire inrush current reduction
ratio has been achived
Yes
End
Fig. 3. Procedure for calculation a specific inrush current
reduction ratio
Fig. 6. Inrush current waveforms with simultaneous energization
of all phases and RN=345.6 Ÿ
Fig. 4. Inrush current waveforms when no mitigation method has
been used
For showing the usefulness of the sequential phase
energization, a simultaneous energization of all phases
with RN=345.6Ÿ KDV EHHQ VLPXODWHG 7KH ZDYHIRUPV RI
the inrush currents of all phases have shown in Fig. 6. As
seen from the figure, simultaneous energization is not
effective as sequential energization (Fig. 5) that has a delay
between energization of each phase.
Fig. 7 shows change of the neutral resistor as a
function of inrush current reduction ratio. As seen from the
figure, for more reduction in inrush current amplitude
Fig. 7. Change of the neutral resistor as a function of inrush
current reduction ratio
Conclusions
The peak of inrush current in the first phase
energization is the highest among the three phases when
sequential phase energization technique is used. Because,
the neutral resistor that is used in this technique has an
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Received 2010 08 15
important role, analytical formulas with considering
neutral resistance have been derived to calculate inrush
current amplitude in the first energization. For,
investigation of the validity of the analytical formulas, a
typical three-phase transformer constructed of single-phase
transformers selected. Then, using the analytical formulas,
a neutral resistor for 30% inrush current reduction ratio
was obtained and applied to the neutral point of the
transformer. Simulation results show the usefulness of the
analytical formulas.
References
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simulation of three-phase transformers for inrush current
studies // IEEE Proc. Gener. Transm. Distribution, 2005. –
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model of transformers based on structure parameters // IEEE
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Jiles–Atherton model parameters and their application to
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Magnetics, 2008. – Vol. 44. – No. 3. – P. 340-345.
M. Jamali, M. Mirzaie, S. Asghar-Gholamian. Mitigation of Magnetizing Inrush Current using Sequential Phase Energization
Technique // Electronics and Electrical Engineering. – Kaunas: Technologija, 2011. – No. 2(108). – P. 67–70.
Energization of a transformer under no load or lightly loaded conditions may result in inrush current with high amplitude that can be
comparable with the fault currents. These currents have undesirable effects, including malfunction of the differential relay, mechanical
and thermal stresses on transformer and reduced power quality of the system. In this paper, a sequential phase energization technique
has been used to mitigate magnetizing inrush current in a grounded system. Because in this technique, the size of the resistor, which is
connected to the neutral point of the transformer, has an important role, analytical formulas have been derived to calculate inrush current
amplitude with a neutral resistor. These analytical formulas have been implemented in the M-File of the MATLAB software for
calculation of different inrush current reduction ratio. Then for the verification of the results, the obtained neutral resistor has been
applied to the equivalent circuit of a typical three-phase transformer and inrush current reduction has been determined by MATLAB
SIMULINK. Ill. 7, bibl. 13 (in English; abstracts in English and Lithuanian).
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PHWRGą // Elektronika ir elektrotechnika. – Kaunas: Technologija, 2011. – Nr. 2(108). – P. 67–70.
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